Let I be a homogeneous ideal of S= K x_1, ..., x_n S= K x 1,…, xn and let J be an initial ideal
of I with respect to a term order. We prove that if J is radical then the Hilbert functions of the …

A glimpse to most of the old and new results on very well-covered graphs from the viewpoint of
commutative algebra | Research in the Mathematical Sciences Skip to main content …

We consider how $ f $-vectors of Cohen--Macaulay and vertex decomposable flag
complexes in geometric settings decompose and interact with geometric transformations …

We show that there are $ f $-vectors of balanced simplicial complexes giving a source of
simplicial complexes exhibiting Boolean a decomposition similar to a geometric Lefschetz …

Given a reciprocal/palindromic polynomial of even degree, we show that the gamma vector
is essentially given by an inverted Chebyshev polynomial basis expansion. As an immediate …

Most applications of the hard Lefschetz theorem related to combinatorial properties of
simplicial complexes involve their $ h $-vectors. In the context of positivity properties …

Let $ S $ be a standard graded polynomial ring over a field, and $ I $ be a homogeneous
ideal that contains a regular sequence of degrees $ d_1,\ldots, d_n $. We prove the …

In this paper, we introduce a new algebraic concept, which we call squarefree P-modules.
This concept is inspired from Karu's proof of the non-negativity of the cd-indices of …

Abstract Let R= S/I be a quotient of a standard graded polynomial ring S by an ideal I
generated by quadrics. If R is Koszul, a question of Avramov, Conca, and Iyengar asks …

Let S be a polynomial ring over a field and I⊆ S a homogeneous ideal containing a regular
sequence of forms of degrees d 1,…, d c. In this paper we prove the Lex-plus-powers …